| Issue |
ESAIM: M2AN
Volume 56, Number 6, November-December 2022
|
|
|---|---|---|
| Page(s) | 2051 - 2079 | |
| DOI | https://doi.org/10.1051/m2an/2022058 | |
| Published online | 14 September 2022 | |
A C0 Interior Penalty Discontinuous Galerkin Method and an equilibrated a posteriori error estimator for a nonlinear fourth order elliptic boundary value problem of p-biharmonic type
1
Department of Mathematics, University of Augsburg, Augsburg, Germany
2
Department of Mathematics, University of Houston, Houston, TX, USA
* Corresponding author: rohop@math.uh.edu
Received:
8
December
2021
Accepted:
5
July
2022
We consider a C0 Interior Penalty Discontinuous Galerkin (C0IPDG) approximation of a nonlinear fourth order elliptic boundary value problem of p-biharmonic type and an equilibrated a posteriori error estimator. The C0IPDG method can be derived from a discretization of the corresponding minimization problem involving a suitably defined reconstruction operator. The equilibrated a posteriori error estimator provides an upper bound for the discretization error in the broken W2,p norm in terms of the associated primal and dual energy functionals. It requires the construction of an equilibrated flux and an equilibrated moment tensor based on a three-field formulation of the C0IPDG approximation. The relationship with a residual-type a posteriori error estimator is studied as well. Numerical results illustrate the performance of the suggested approach.
Mathematics Subject Classification: 35K35 / 35K55 / 65M60
Key words: C0 Interior Penalty Discontinuous Galerkin approximation / nonlinear fourth order elliptic problem of p-biharmonic type / a posteriori error estimation / equilibration
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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